Autocorrelation analysis of NOESY data provides residue compactness for folded and unfolded proteins

A novel spectral entropy interpretation for protein NOESY data is presented for the investigation of the spatial distribution of residues in protein structures without the requirement of NOE cross peak assignments. In this approach individual traces S(i)(omega) from a 3D (15)N NOESY-HSQC taken at frequency positions corresponding to different amide groups (residue position i) are subjected to a self-convolution procedure thus leading to the autocorrelation function C(i)(omega) of the NOESY-trace for a particular backbone residue position. The characteristic spatial surrounding of a particular residue position is reflected in the corresponding autocorrelation function and can be quantified by taking the (spectral) entropy S(nu) as an information measure. The feasibility of this novel approach is demonstrated with applications to the proteins Cyclophilin D and Osteopontin and the protein complex between the lipocalin Q83 and the bacterial siderophore Enterobactin. Typically, large entropy values were found for residues located in structurally loosely defined regions, whereas small entropy values were found for residues in hydrophobic core regions of the protein with tightly interacting side chains and distinct chemical shift patterns. The applications to the unfolded Osteopontin and the Q83/Enterobactin protein complex indicated that both local compaction of the polypeptide chain due to transiently formed structural elements and subtle changes in side-chain packing can be efficiently probed by this novel approach.